14edo: Difference between revisions
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14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a [[triad]]-rich 9-note [[mos scale]] of [[5L 4s]], wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad. | 14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a [[triad]]-rich 9-note [[mos scale]] of [[5L 4s]], wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad. | ||
14edo contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Octave stretch === | === Octave stretch === | ||
14edo benefits from [[octave stretch]] as harmonics 3, 7, and 11 are all tuned flat. [[22edt]] and [[ | 14edo benefits from [[octave stretch]] as harmonics 3, 7, and 11 are all tuned flat. [[22edt]], [[36ed6]] and [[42zpi]] are among the possible choices. | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
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! Approximate<br>Ratios 2 <ref group="note">Based on treating 14edo as an 11-limit temperament of {{val| 14 22 32 39 48}} (14c).</ref> | ! Approximate<br>Ratios 2 <ref group="note">Based on treating 14edo as an 11-limit temperament of {{val| 14 22 32 39 48}} (14c).</ref> | ||
! Approximate<br>Ratios 3 <ref group="note">Nearest 15-odd-limit intervals by [[direct approximation]].</ref> | ! Approximate<br>Ratios 3 <ref group="note">Nearest 15-odd-limit intervals by [[direct approximation]].</ref> | ||
! colspan="3" | [[Ups and | ! colspan="3" | [[Ups and downs notation]] | ||
! Interval Type | ! Interval Type | ||
! Audio | ! Audio | ||
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| [[File:piano_1_1edo.mp3]] | | [[File:piano_1_1edo.mp3]] | ||
|} | |} | ||
<references group="note" /> | |||
=== Sagittal notation === | === Sagittal notation === | ||
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0-3-8-11 = C vE G vB = Cv7 = C down-seven | 0-3-8-11 = C vE G vB = Cv7 = C down-seven | ||
For a more complete list, see [[Ups and | For a more complete list, see [[Ups and downs notation #Chords and Chord Progressions]]. | ||
== Approximation to JI == | == Approximation to JI == | ||
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==== Selected 13-limit intervals ==== | ==== Selected 13-limit intervals ==== | ||
[[File:14ed2-001.svg|alt=alt : Your browser has no SVG support.]] | [[File:14ed2-001.svg|alt=alt : Your browser has no SVG support.]] | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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| Sagugu | | Sagugu | ||
| Diaschisma | | Diaschisma | ||
|- | |||
|7 | |||
|[[21/20]] | |||
|[-2 1 -1 1⟩ | |||
|84.47 | |||
|Zogu | |||
|Chroma | |||
|- | |- | ||
| 7 | | 7 | ||
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| Island comma | | Island comma | ||
|} | |} | ||
<references group="note" /> | |||
== Scales == | == Scales == | ||
=== MOS scales === | |||
{{Main|List of MOS scales in {{PAGENAME}}}} | {{Main|List of MOS scales in {{PAGENAME}}}} | ||
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[[File:Screen Shot 2020-04-23 at 11.47.30 PM.png|none|thumb|870x870px|5\14 MOS using 1L 1s, 2L 1s, 3L 2s, 3L 5s, 3L 8s]] | [[File:Screen Shot 2020-04-23 at 11.47.30 PM.png|none|thumb|870x870px|5\14 MOS using 1L 1s, 2L 1s, 3L 2s, 3L 5s, 3L 8s]] | ||
=== Beep[9] === | ==== Beep[9] ==== | ||
14edo is also the largest edo whose patent val [[support]]s [[beep]] temperament, tempering out the chromatic semitone (21:20), and falling toward the "brittle" (fifths wider than in 9edo) end of that spectrum. beep is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres ("bell-like" or opaque-sounding ones probably work best). beep forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Beep[9] has similarities to mavila, slendro, and pelog scales as well. | 14edo is also the largest edo whose patent val [[support]]s [[beep]] temperament, tempering out the chromatic semitone (21:20), and falling toward the "brittle" (fifths wider than in 9edo) end of that spectrum. beep is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres ("bell-like" or opaque-sounding ones probably work best). beep forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Beep[9] has similarities to mavila, slendro, and pelog scales as well. | ||
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* 13\14: Major 9th<sub>9</sub>: A high, incisive leading tone. | * 13\14: Major 9th<sub>9</sub>: A high, incisive leading tone. | ||
* 14\14: The 10th<sub>9</sub> or "enneatonic decave" (i. e. the octave, 2:1). | * 14\14: The 10th<sub>9</sub> or "enneatonic decave" (i. e. the octave, 2:1). | ||
=== Others === | |||
* 2 2 2 2 2 2 2 - [[Equiheptatonic]] (exactly [[7edo]]) | |||
* 2 2 2 2 1 4 1 - Fennec{{idiosyncratic}} (original/default tuning) | |||
* 1 4 1 2 2 2 2 - Inverse fennec{{idiosyncratic}} (original/default tuning) | |||
* 3 1 4 1 4 1 - Pseudo-[[augmented]] | |||
* 1 4 1 2 1 4 1 - Pseudo-double harmonic minor | |||
== Diagrams == | == Diagrams == | ||
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== See also == | == See also == | ||
* [[Lumatone mapping for 14edo]] | * [[Lumatone mapping for 14edo]] | ||
* [[MisterShafXen’s take on 14edo harmony]] | |||
== Further reading == | == Further reading == | ||
[[File:Libro_Tetradecafónico.PNG|alt=Libro_Tetradecafónico.PNG|Libro_Tetradecafónico.PNG|thumb|''Tetradecaphonic Scales for Guitar'' cover art.]] | [[File:Libro_Tetradecafónico.PNG|alt=Libro_Tetradecafónico.PNG|Libro_Tetradecafónico.PNG|thumb|''Tetradecaphonic Scales for Guitar'' cover art.]] | ||
* [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Tetradecaphonic Scales for Guitar: Scales, Chord-Scales, Notation, and Theory for Fourteen Equal Divisions of the Octave]''. 2009. | * [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Tetradecaphonic Scales for Guitar: Scales, Chord-Scales, Notation, and Theory for Fourteen Equal Divisions of the Octave]''. 2009. | ||
[[Category:14edo| ]] <!-- main article --> | [[Category:14edo| ]] <!-- main article --> | ||